Spectral asymptotics for arithmetic quotients of SL(n,R)/SO(n)

Abstract

In this article we study the asymptotic distribution of the cuspidal spectrum of arithmetic quotients of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$. In particular, we obtain Weyl's law with an estimation on the remainder term. This extends some of the main results of Duistermaat, Kolk, and Varadarajan ([DKV1]) to this setting